Sexton's half-back partner Conor Murray was pleased with how Ireland put the game beyond the visitors' reach, having been locked in a real arm wrestle for 50 to 60 minutes.
"It is just the consistency element that we are often criticised for, and rightly so," said Murray. "That is what we have targeted in camp and chatted about it and how we can fix that.
"The second half has a big part to play in that, keep the scoreboard ticking over. That was a little chat we had at half-time, to make sure we keep on playing, keeping the ball in hand and keep going for it."
Heaslip, who captained Ireland in the absence of an ill Paul O'Connell, revealed afterwards that Joe Schmidt had 'a couple of choice words' for his winning side in the dressing room.
Murray said that is just the way the meticulous New Zealander is - already targeting the improvements that will be necessary when defending champions Wales coming calling.
"You are not going to go around patting each other on the back after a win like that. There are areas that didn't work quite well, things that didn't come off," admitted the Limerick man.
"So, there's always things to improve on and that is a good mindset to have as a coach. You are not going to get carried away (after today).
"There's always something to work on, you can't think you are on top of the world after beating Scotland. There's always plenty to improve."
Next up for Ireland is the visit of Wales next Saturday and having been on the Lions tour with a number of Welsh players, Murray is well-placed to assess the Dragons.
Warren Gatland's men may have stuttered past Italy in their Championship opener, but Murray knows the sides' round 2 showdown is going to be another step up in intensity.
"Wales are a completely different team. They will offer completely different threats that we are going to have to try and nullify.
"It is a completely different set-up this week against Wales. They struggled a little bit in the first half (against Italy) and then they seemed like they weren't in top gear at times.
"They still managed to get through yesterday. We know how good they are and especially from the summer, the threats they bring from all over the park. It is going to be a tough one."
Murray is enjoying the working relationship he is developing with Schmidt, who is constantly striving to challenge his players and get the best out of them.
"We have had a few get-togethers and there would be a few phonecalls here and there if there is something that you need to work on," he explained.
"At the same time you are back with your province and you are concentrating on Europe or the Rabo and he does give you that space as well. If he feels the need to contact you and maybe tell you to improve on something, that is okay. It will only benefit your province as well.
"Joe has a great knowledge of each player and what your strengths and weaknesses are, so he is always chatting to you and trying to get your point of view on certain aspects of the game. He gives me little things to work on and I'm enjoying it.
"Whether it be my passing, kicking or how I read the game, he has given me things to work on, how I see the game unfolding and how I can influence things."
Reflecting on some of the positives from today's 28-6 victory, Murray highlighted Ireland's solid defence which kept Scotland try-less throughout and the strong finishes to both halves that they produced.
"With Rob's try we held onto the ball and Scotland were making it difficult for us for large portions of the game at the breakdown, slowing down our ball and we knew it would take a good number of phases to break them down and that is what happened. That is a pleasing aspect.
"We kept them out a number of times in the first half. They nearly snuck in at the corner at one stage (through David Denton).
"We had good confidence in our defence at that time and then to go back up and obviously for Trimby to get through was a nice way to finish the first half and go in on a high which was pretty important.
"It's never in the bag out there. You always feel under pressure and we wanted to keep playing, developing our game and try to hold onto the ball, get through our phases and create more chances. There are things to work on, but at times we did feel quite good."